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50 is Divided into Two Parts such that the Sum of their Reciprocals is 1/12. Find the Two Parts.

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Explanation

  • 50 is divided into two parts.
  • The sum of their reciprocals is 1/12.

Two numbers can be calculate in this way.

Let suppose 50 is divided into y and z.

y + z = 50 ________ (i)

The sum of their reciprocals is 1/12.

1/y + 1/z = 1/12 ________ (ii)

Solving (i) and (ii) simultaneously we can easily figure out the required numbers

To Find

Number = ?

Solution

Let suppose 50 is divided into y and z.

y + z = 50 ________ (i)

The sum of their reciprocals is 1/12.

1/y + 1/z = 1/12

12 (z + y) = yz ________ (ii)

Putting value of equation (i) and (ii)

12(50) = yz

600 = yz

600/y = z

putting in equation (i)

y + 600/y = 50

y2 + 600 = 50y

y2 – 50y + 600 = 0

y2 – 30y – 20y + 600 = 0

y (y – 30) – 20 (y – 30) = 0

(y – 30)(y – 20) = 0

y = 30        or      y = 20

putting in equation (i)

30 + z = 50

z = 50 – 30

z = 20

or

20 + z = 50

z = 50 – 20

z = 30

Required Numbers = 20 and 30 answer

Conclusion

50 is divided into two parts such that the sum of their reciprocals is 1/12. The numbers will be 20 and 30.

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